Finite Group Databasebeta

← C2×#15689398 #20253101

Subgroups — C2×#15689398 #20253101

Order 6016.

448 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094054C212yesmaximal
2C22×Dic188C211yesmaximal, characteristic, complemented
3#15689398C218yesmaximal, direct product factor
4C2×#13093960C211yesmaximal, characteristic, complemented
5C2×#13093942C212yesmaximal, complemented
6C2×#131×C47C211yesmaximal, characteristic
7C22×Dic94C2212yes—
8#13094054—24no—
9#13094054C2218yes—
10C2×Dic188—21no—
11C2×Dic188—21no—
12C2×Dic188—22no—
13C2×Dic188C2214yescomplemented
14C2×#10625337—22no—
15C2×#10625335—22no—
16C2×#10625329C2212yes—
17#13093960C2214yescomplemented
18#13093942C2218yescomplemented
19C2×#41×C47C2211yescharacteristic
20#131×C47—22no—
21#131×C47C2214yes—
22C2×M16×C47—21no—
23C2×M16×C47C2211yescharacteristic
24C22×C8×C47—21no—
25C22×C8×C47C2211yescharacteristic
26#41×C47—21no—
27#41×C47—21no—
28#41×C47D412yes—
29#41×C47C2312yes—
30C2×Q8×C47D411yescharacteristic
31C2×D4×C47—21no—
32C2×D4×C47D411yescharacteristic
33C22×C4×C47—21no—
34C22×C4×C47C2311yescharacteristic
35C22×Dic47—22no—
36C2×Dic94—22no—
37C2×Dic94—22no—
38C2×Dic94—22no—
39C2×Dic94—22no—
40C2×Dic94—22no—
41C2×Dic94C2314yes—
42M16×C47—21no—
43M16×C47—24no—
44M16×C47C2312yes—
45C2×C8×C47—21no—
46C2×C8×C47—24no—
47C2×C8×C47D411yescharacteristic
48C2×C8×C47D411yescharacteristic
49C2×C8×C47D412yes—
50C2×C8×C47C2312yes—
51#10625337—28no—
52#10625335—28no—
53#10625329—22no—
54#10625329C2314yes—
55C2×C47⋊C8—22no—
56Dic188—24no—
57Dic188—24no—
58C23×C47—21no—
59C23×C47#4111yescharacteristic
60Q8×C47—21no—
61Q8×C47C2×D412yes—
62D4×C47—22no—
63D4×C47—22no—
64D4×C47—21no—
65D4×C47C2×D412yes—
66C2×C4×C47—21no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47#4111yescharacteristic
74C2×C4×C47C2411yescharacteristic
75C2×Dic47—24no—
76C2×Dic47—42no—
77C2×Dic47—42no—
78Dic94—24no—
79Dic94—24no—
80Dic94—42no—
81Dic94—42no—
82C8×C47—22no—
83C8×C47C2×D412yes—
84C8×C47C2×D412yes—
85C47⋊C8—24no—
86C22×C47—22no—
87C22×C47—22no—
88C22×C47—42no—
89C22×C47#12111yescharacteristic
90C22×C47#12111yescharacteristic
91C22×C47C2×#4111yescharacteristic
92C4×C47—22no—
93C4×C47#12111yescharacteristic
94C4×C47#12111yescharacteristic
95C4×C47C22×D411yescharacteristic
96C4×C47C22×D411yescharacteristic
97Dic47—44no—
98C2×#473—471nomaximal, Sylow
99C2×C47—21no—
100C2×C47—21no—
101C2×C47—42no—
102C2×C47#47312yescomplemented
103C2×C47C2×#12111yescharacteristic
104C2×#137—472no—
105C22×Q16—471no—
106C2×#131D4711yescharacteristic
107#473—478no—
108C2×#108—471no—
109C2×#101—472no—
110C47C2×#47311yescharacteristic, complemented, Sylow
111C2×#41C2×D4711yescharacteristic
112C22×Q8—472no—
113#137—478no—
114#137—944no—
115C2×Q16—474no—
116C2×Q16—942no—
117C2×Q16—941no—
118C2×Q16—941no—
119C2×Q16—942no—
120C2×SD16—942no—
121#131—22no—
122#131C2×D4714yes—
123C2×M16—21no—
124C2×M16—472no—
125C2×M16C2×D4711yescharacteristic
126C22×C8—21no—
127C22×C8C2×D4711yescharacteristic
128#108—474no—
129#101—478no—
130#41—21no—
131#41—21no—
132#41D18812yes—
133#41C22×D4712yes—
134C2×Q8—474no—
135C2×Q8—942no—
136C2×Q8—942no—
137C2×Q8—942no—
138C2×Q8—942no—
139C2×Q8—942no—
140C2×Q8D18811yescharacteristic
141C2×D4—21no—
142C2×D4D18811yescharacteristic
143C22×C4—21no—
144C22×C4—942no—
145C22×C4C22×D4711yescharacteristic
146Q16—948no—
147Q16—944no—
148Q16—944no—
149SD16—948no—
150M16—21no—
151M16—24no—
152M16—474no—
153M16—942no—
154M16C22×D4712yes—
155C2×C8—21no—
156C2×C8—24no—
157C2×C8—942no—
158C2×C8C22⋊D4711yescharacteristic
159C2×C8C22⋊D4711yescharacteristic
160C2×C8C22⋊D4712yes—
161C2×C8C22×D4712yes—
162C23—21no—
163C23#1062535011yescharacteristic
164Q8—21no—
165Q8—944no—
166Q8—944no—
167Q8—1882no—
168Q8—1882no—
169Q8C2×D18812yes—
170D4—22no—
171D4—22no—
172D4—21no—
173D4C2×D18812yes—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—944no—
178C2×C4—1882no—
179C2×C4—1882no—
180C2×C4C2×D18811yescharacteristic
181C2×C4C2×D18811yescharacteristic
182C2×C4#1062535011yescharacteristic
183C2×C4C2×C22⋊D4711yescharacteristic
184C2×C4C2×C22⋊D4711yescharacteristic
185C2×C4C23×D4711yescharacteristic
186C8—22no—
187C8—944no—
188C8C2×C22⋊D4712yes—
189C8C2×C22⋊D4712yes—
190C22—22no—
191C22—22no—
192C22—42no—
193C22#1309399811yescharacteristic
194C22#1309399811yescharacteristic
195C22C2×#1062535011yescharacteristic
196C4—22no—
197C4—1884no—
198C4#1309399811yescharacteristic
199C4#1309399811yescharacteristic
200C4C22×C22⋊D4711yescharacteristic
201C4C22×D18811yescharacteristic
202C2—21no—
203C2—21no—
204C2—42no—
205C2#1568939812yesdirect product factor
206C2C2×#1309399811yescharacteristic
subgroupG/H
centerC22#13093998
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#131×C47C2
socleC22×C47#121
hypercenterC2×#131D47
hypocenterC47C2×#473
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×Dic188C2semidirect
3. #15689398C2direct (N × H)
4. C2×#13093960C2semidirect
5. C2×#13093942C2semidirect
13. C2×Dic188C22semidirect
17. #13093960C22semidirect
18. #13093942C22semidirect
102. C2×C47#473semidirect
110. C47C2×#473semidirect
205. C2#15689398direct (N × H)